Convolution operators on group algebras which are tauberian or cotauberian
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2018Derechos
Attribution-NonCommercial-NoDerivatives 4.0 International
Publicado en
Journal of Mathematical Analysis and Applications (2018) Vol.465, Issue 1, pp. 309-317
Editorial
Academic Press Inc.
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Palabras clave
Multiplier
Tauberian operator
Convolution operator
Resumen/Abstract
ABSTRACT: We study the convolution operators Tμ acting on the group algebras L1(G) and M(G), where G is a locally compact abelian group and μ is a complex Borel measure on G. We show that a cotauberian convolution operator Tμ acting on L1(G) is Fredholm of index zero, and that Tμ is tauberian if and only if so is the corresponding convolution operator acting on the algebra of measures M(G), and we give some applications of these results.
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